Abstract
We offer a novel perspective on \( \mathcal{N} \) = 4 supersymmetric Yang-Mills (SYM) theory through the framework of the Nicolai map, a transformation of the bosonic fields that allows one to compute quantum correlators in terms of a free, purely bosonic functional measure. Generally, any Nicolai map is obtained through a path-ordered exponential of the so-called coupling flow operator. The latter can be canonically constructed in any gauge using an \( \mathcal{N} \) = 1 off-shell superfield formulation of \( \mathcal{N} \) = 4 SYM, or alternatively through dimensional reduction of the result from \( \mathcal{N} \) = 1 D = 10 SYM, in which case we need to restrict to the Landau gauge. We propose a general theory of the \( \mathcal{N} \) = 4 coupling flow operator, arguing that it exhibits an ambiguity in form of an R-symmetry freedom given by the Lie algebra \( \mathfrak{su} \)(4). This theory incorporates our two construction approaches as special points in \( \mathfrak{su} \)(4) and defines a broad class of Nicolai maps for \( \mathcal{N} \) = 4 SYM.
Article PDF
Similar content being viewed by others
References
H. Nicolai, On a New Characterization of Scalar Supersymmetric Theories, Phys. Lett. B 89 (1980) 341 [INSPIRE].
H. Nicolai, Supersymmetry and Functional Integration Measures, Nucl. Phys. B 176 (1980) 419 [INSPIRE].
H. Nicolai, Supersymmetric functional integration measures, lectures delivered at the NATO Advanced Study Institute on Supersymmetry, Bonn, Germany, 20–31 Aug 1984, CERN-TH-4010, K. Dietz et al. eds., Plenum Press (1984) pp.393-420.
O. Lechtenfeld, Construction of the Nicolai mapping in supersymmetric field theories, Ph.D. thesis, Bonn University (1984), internal report BONN-IR-84-42, ISSN-0172-8741.
R. Flume and O. Lechtenfeld, On the Stochastic Structure of Globally Supersymmetric Field Theories, Phys. Lett. B 135 (1984) 91 [INSPIRE].
K. Dietz and O. Lechtenfeld, Nicolai Maps and Stochastic Observables From a Coupling Constant Flow, Nucl. Phys. B 255 (1985) 149 [INSPIRE].
K. Dietz and O. Lechtenfeld, Ghost free quantization of non-Abelian gauge theories via the Nicolai transformation of their supersymmetric extensions, Nucl. Phys. B 259 (1985) 397 [INSPIRE].
S. Ananth, H. Nicolai, C. Pandey and S. Pant, Supersymmetric Yang-Mills theories:not quite the usual perspective, J. Phys. A 53 (2020) 17 [arXiv:2001.02768] [INSPIRE].
H. Nicolai and J. Plefka, N = 4 super-Yang-Mills correlators without anticommuting variables, Phys. Rev. D 101 (2020) 125013 [arXiv:2003.14325] [INSPIRE].
S. Ananth, O. Lechtenfeld, H. Malcha, H. Nicolai, C. Pandey and S. Pant, Perturbative linearization of supersymmetric Yang-Mills theory, JHEP 10 (2020) 199 [arXiv:2005.12324] [INSPIRE].
S. Ananth, H. Malcha, C. Pandey and S. Pant, Supersymmetric Yang-Mills theory in D = 6 without anticommuting variables, Phys. Rev. D 103 (2021) 025010 [arXiv:2006.02457] [INSPIRE].
O. Lechtenfeld and M. Rupprecht, Universal form of the Nicolai map, Phys. Rev. D 104 (2021) L021701 [arXiv:2104.00012] [INSPIRE].
O. Lechtenfeld and M. Rupprecht, Construction method for the Nicolai map in supersymmetric Yang–Mills theories, Phys. Lett. B 819 (2021) 136413 [arXiv:2104.09654] [INSPIRE].
H. Malcha and H. Nicolai, Perturbative linearization of super-Yang-Mills theories in general gauges, JHEP 06 (2021) 001 [arXiv:2104.06017] [INSPIRE].
O. Lechtenfeld and H. Nicolai, A perturbative expansion scheme for supermembrane and matrix theory, JHEP 02 (2022) 114 [arXiv:2109.00346] [INSPIRE].
O. Lechtenfeld, Stochastic variables in ten-dimensions?, Nucl. Phys. B 274 (1986) 633 [INSPIRE].
J. Wess and J. Bagger, Supersymmetry and supergravity, Princeton University Press, U.S.A. (1992).
L. Brink, J.H. Schwarz and J. Scherk, Supersymmetric Yang-Mills Theories, Nucl. Phys. B 121 (1977) 77 [INSPIRE].
S. Kovacs, N = 4 supersymmetric Yang-Mills theory and the AdS/SCFT correspondence, Ph.D. thesis, (1999) [hep-th/9908171] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2111.13223
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Rupprecht, M. The coupling flow of \( \mathcal{N} \) = 4 super Yang-Mills theory. J. High Energ. Phys. 2022, 4 (2022). https://doi.org/10.1007/JHEP04(2022)004
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2022)004